Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D17×#89204 |
| unambiguous semidirect product | C17⋊(C22×#89204) |
| unambiguous semidirect product | (C2×C17)⋊(C2×#89204) |
| derived, Hall | C72×C17 ⋊ C22×C9 |
| Hall | C17×#89204 ⋊ C22 |
| Hall | C2×C72×D17 ⋊ C9 |
| Sylow | C72 ⋊ C2×C9×D17 |
| Sylow | C17 ⋊ C22×#89204 |
300 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14994 |
1140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 216);